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interesting function

Source: 9th EMC, 12th December 2020 - 20th December 2020, SENIOR league, P4.

December 22, 2020
algebrafunctional equationfunction

Problem Statement

Let R+\mathbb{R^+} denote the set of all positive real numbers. Find all functions f:R+→R+f: \mathbb{R^+}\rightarrow \mathbb{R^+} such that xf(x+y)+f(xf(y)+1)=f(xf(x))xf(x + y) + f(xf(y) + 1) = f(xf(x)) for all x,y∈R+.x, y \in\mathbb{R^+}.
Proposed by Amadej Kristjan Kocbek, Jakob Jurij Snoj
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